Final answer:
The equation 4(3x+7)-5=12x+8 simplifies to the impossibility 23=8 after canceling out the variable on both sides, indicating that there is no solution, and it is a contradictory equation.
Step-by-step explanation:
To solve the equation 4(3x+7)-5=12x+8, you need to expand the left side and simplify both sides of the equation. First, distribute the 4 into the parentheses:
4 * 3x + 4 * 7 - 5 = 12x + 8
12x + 28 - 5 = 12x +
Now, simplify both sides by combining like terms:
12x + 23 = 12x + 8
Next, let's subtract 12x from both sides to get the variable terms on one side and the constant terms on the other side
12x - 12x + 23 = 12x - 12x + 8
23 = 8
After simplification, we see that the equation reduces to an impossibility (23 does not equal 8), which means that there is no solution. This is an example of a contradictory equation, where the variable 'x' cancels out, and a falsehood remains. This indicates that no value for 'x' will satisfy the original equation.